Ab initio phonon dispersion curves and interatomic force constants of barium titanate

TL;DR

This paper uses first-principles calculations to analyze phonon dispersion and interatomic forces in cubic BaTiO3, revealing atomic displacement correlations responsible for ferroelectric instability and comparing results with experimental data.

Contribution

It provides a detailed ab initio analysis of phonon dispersion in BaTiO3 and introduces a simplified model linking atomic displacements to ferroelectric behavior.

Findings

Phonon dispersion curves match experimental data.

Correlated atomic displacements cause ferroelectric instability.

Weak Ti-O force constants are crucial for ferroelectricity.

Abstract

The phonon dispersion curves of cubic BaTiO_3 have been computed within a first-principles approach and the results compared to the experimental data. The curves obtained are very similar to those reported for KNbO_3 by Yu and Krakauer [Phys. Rev. Lett. 74, 4067 (1995)]. They reveal that correlated atomic displacements along <100> chains are at the origin of the ferroelectric instability. A simplified model illustrates that spontaneous collective displacements will occur when a dozen of aligned atoms are coupled. The longitudinal interatomic force constant between nearest neighbour Ti and O atoms is relatively weak in comparison to that between Ti atoms in adjacent cells. The small coupling between Ti and O displacements seems however necessary to reproduce a ferroelectric instability.